Mathematical subtleties and scientific knowledge: Francis Bacon and mathematics, at the crossing of two traditions.

This article engages the much-debated role of mathematics in Bacon's philosophy and inductive method at large. The many references to mathematics in Bacon's works are considered in the context of the humanist reform of the curriculum studiorum and, in particular, through a comparison with the kinds of natural and intellectual subtlety as they are defined by many sixteenth-century authors, including Cardano, Scaliger and Montaigne. Additionally, this article gives a nuanced background to the 'subtlety' commonly thought to have been eschewed by Bacon and by Bacon's self-proclaimed followers in the Royal Society of London. The aim of this article is ultimately to demonstrate that Bacon did not reject the use of mathematics in natural philosophy altogether. Instead, he hoped that following the Great Instauration a kind of non-abstract mathematics could be founded: a kind of mathematics which was to serve natural philosophy by enabling men to grasp the intrinsic subtlety of nature. Rather than mathematizing nature, it was mathematics that needed to be 'naturalized'.